Properties

Label 14144.y
Number of curves $2$
Conductor $14144$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 14144.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14144.y1 14144be1 \([0, -1, 0, -3809, -89215]\) \(23320116793/2873\) \(753139712\) \([2]\) \(12288\) \(0.72670\) \(\Gamma_0(N)\)-optimal
14144.y2 14144be2 \([0, -1, 0, -3489, -105151]\) \(-17923019113/8254129\) \(-2163770392576\) \([2]\) \(24576\) \(1.0733\)  

Rank

sage: E.rank()
 

The elliptic curves in class 14144.y have rank \(0\).

Complex multiplication

The elliptic curves in class 14144.y do not have complex multiplication.

Modular form 14144.2.a.y

sage: E.q_eigenform(10)
 
\(q + 2 q^{3} - 2 q^{5} - 2 q^{7} + q^{9} - 6 q^{11} + q^{13} - 4 q^{15} + q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.